Algebra 1 Standard Linear Functions Categories Graphs Tables Equations Contet Summative Assessment Date: Friday, September 14 th Page 1
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Linear Functions DAY 1 Notesheet Topic Increasing and Decreasing Graphs Target: I can determine if a graph is increasing or decreasing. Eample 1: Eample 2: Eample 3: Eample 4: Page 4
Linear Functions DAY 1 Notesheet Topic Increasing and Decreasing Graphs Target: I can draw intervals on a graph to determine increasing or decreasing. Eample 5: Eample 6: Eample 7: Eample 8: Page 5
Linear Functions DAY 1 Homework Topic Increasing and Decreasing Graphs Draw intervals on the following graphs to show where they are increasing and decreasing. 1) 2) y y 3) 4) y y 5) 6) Page 6
Linear Functions DAY 2 Notesheet Topic Rate of Change Non-Linear Graphs Linear Graphs y y y y y y y EXAMPLES: For each graph, divide into intervals of increasing, decreasing or neither. Find the rate of change. Using that information, decide whether the graph is linear. Rate of Change: Rate of Change: Rate of Change: Linear: Yes No Linear: Yes No Linear: Yes No EXAMPLES: Using our new vocabulary (increasing, decreasing, rate of change) compare the two graphs below by finding a similarity and difference. Similarity: Difference: Page 7
Linear Functions DAY 2 Homework Topic Rate of Change #1-6: For each graph, divide into intervals of increasing, decreasing or neither. Find the rate of change. Using that information, decide whether the graph is linear or non-linear. 1. 2. 3. Rate of Change: Rate of Change: Rate of Change: Linear Non-linear Linear Non-linear Linear Non-linear 4. 5. 6. Rate of Change: Rate of Change: Rate of Change: Linear Non-linear Linear Non-linear Linear Non-linear #7-10: Using our new vocabulary (increasing, decreasing, rate of change) compare each set of graphs below by finding a similarity and difference. 7. Graph A Graph B Similarity: Difference: Page 8
Linear Functions DAY 2 Homework Topic Rate of Change 8. Graph C Graph D Similarity: Difference: 9. Graph E Graph F Similarity: Difference: 10. Graph G Graph H Similarity: Difference: Page 9
Linear Functions DAY 3 Notesheet Topic Linear Tables Circle the line that is steeper. Then find the slope of each one. Slope = Slope = Slope = Slope = The " " or the " " tells us how a line is. Ignore the and look the. The the number, the Slope = Slope = the line. If the slope is, the line. If the slope is, the line. Rate of Change Formulas Page 10
Linear Functions DAY 3 Notesheet Topic Linear Tables Answer the following questions about each table 1) Is the function increasing, decreasing, both, or neither? 2) Is the rate of change constant or not constant? 3) Is the function linear or non-linear? 4) If linear, calculate the rate of change. For the following questions give a similarity and a difference each table. Use words such as increasing, decreasing, and rate of change. Similarity: Difference: Similarity: Difference: Similarity: Difference: Page 11
Linear Functions DAY 3 Homework Topic Linear Tables For numbers 1-6, use the tables below. A B C D E F 1. Which tables are always increasing? 2. Which tables are always decreasing? 3. Which tables are not increasing and not decreasing? 4. Which tables are both increasing and decreasing? 5. Which tables have a constant rate of change? 6. Which tables are linear? For numbers 7-8, use the tables below. Each table IS LINEAR FUNCTION. A B C 7. What is the rate of change of Function A? Function B? Function C? 8. Which linear function has the steepest graph and which linear function s graph is least steep? Page 12
Linear Functions DAY 3 Homework Topic Linear Tables For numbers 9-14, the tables below came from the tables on the front page. Answer each question using the following words, increasing, decreasing, and rate of change. A B 9. Give a similarity between Function A and Function B. 10. Give two differences between Function A and Function B. D F 11. Give a similarity between Function D and Function F. 12. Give a difference between Function D and Function F. C F 13. Give a similarity between Function C and Function F. 14. Give a difference between Function C and Function F. Page 13
Linear Functions DAY 4 Notesheet Topic Linear Equations All functions can be modeled with... What makes a graph linear? What makes a table linear? Page 14
Linear Functions DAY 4 Notesheet Topic Linear Equations Note: Tables on bottom right to help make graphs Equation: Linear or non: Equation: Linear or non: Equation: Linear or non: Equation: Linear or non: Equation: Linear or non: Page 15
Linear Functions DAY 4 Notesheet Topic Linear Equations Linear Equations: Non-Linear Equations: Can NOT have any Can NOT have an symbol Can NOT have in the The most common linear equation is. y = where m = b= Identify the in the following equations. y = 3 + 9 y = + 4 y = 5 2 y = 0.25 3 2 y = + 4 3 y = 15 Match the graph with the correct equation. Page 16
Linear Functions DAY 4 Homework Topic Linear Equations Determine if the following equations are linear or non-linear. 1.) 1.75 3 17 2.) 5 3 3.) 30 1.75 4.) 5.) h() = 3 17 7 6.) 7.) 3.5 1.07 8.) 2 7y = 14 9.) 2 1 10.) 11 11.) 5.25 150 12.) 10,000 2 Identify the rate of change in the following equations. 13.) 9 14.) 0.88 10 15.) 1 16.) 10 17.) 40 18.) 5 Page 17
Linear Functions DAY 4 Homework Topic Linear Equations For the following graphs: a)determine if the graph is linear or non-linear b)determine if the graph is increasing and/or decreasing and mark the intervals a) a) a) b) b) b) a) a) a) b) b) b) a) a) a) b) b) b) Page 18
Linear Functions DAY 5 Notesheet Topic Recognizing Linear Relationships in Contet Eample 1 This school year you decide to tutor one of your neighbors who is in 6 th grade. The 6 th grader s parents are willing to give you $10 an hour for your services. Does the amount of money you make and the number of hours you work represent a linear relationship? How do you know? Is this a linear relationship? Why (or why not)? Can you predict how much money you will have if you work 40 hours over the course of the school year? Eample 2 The number of students at Parkway Central High School breaks down in the following way: 290 freshman, 276 sophomores, 262 juniors, and 248 seniors. Does the number of students and the grade level of the students form a linear relationship? How do you know? Is this a linear relationship? Why (or why not)? Can you predict how many students would be in the 8 th grade class? IMPORTANT: What are steps to determining if the word problem shows linear relationship? Page 19
Linear Functions DAY 5 Notesheet Topic Recognizing Linear Relationships in Contet Algebra Skill Review Making a table using percentages Complete the table by going up by 20% Complete the table by going up by 5% 1 1000 1 40 2 2 3 3 4 4 5 5 Complete the table by going down by Complete the table by going down by 1 800 1 150 2 2 3 3 4 4 5 5 Eample 3 The population of Wentzville, Missouri, has been increasing at a rate of 15% over the past few years. It is epected to continue increasing by 15% for the net few years as well. The population of Wentzville was 120,000 people in 2010. Does the number of people and the number of years since 2010 form a linear relationship? How do you know? Is this a linear relationship? Why (or why not)? Can you predict how big the population would be in 2017? Page 20
Linear Functions DAY 5 Notesheet Topic Recognizing Linear Relationships in Contet Eample 4 To rent a bulldozer a company charges a deposit of $400 and an additional $50 per hour while it is in use. Does the amount of time you rent the bulldozer and the amount of money you spend represent a linear relationship? How do you know? Is this a linear relationship? Why (or why not)? Can you predict how long you could rent the bulldozer if you had $830 to spend? Eample 5 You bought a new video game over the summer and you played it for 12 hours the first day! However, like most things, they get boring. So each day you played half as much as the day before. Does the number of days and the number of hours playing your video game represent a linear relationship? How do you know? Is this a linear relationship? Why (or why not)? Can you predict how long you will play the game (in minutes or seconds) after 8 days? Page 21
Linear Functions DAY 5 Homework Topic Recognizing Linear Relationships in Contet 1. Right now there is $50 in your savings account (August) and starting net month you plan to put in $15 each month. Does the number of months and the amount of money saved represent a linear relationship? Justify your answer. If it is linear, can you predict how long it will take you to have saved $100? 2. Your parents just bought a new car that cost $15,000. The amount of money that the car is actually worth (it s value) goes down by 15% each year for the net few years. Does the number of years and the amount of money the car is worth represent a linear relationship? Justify your answer. If it is linear, can you predict the value of the car in 5 years? 3. The local ice cream shop has a menu that allows you to buy ice cream cones and charges you different prices based on the number of scoops you want. Their prices include a 1-scoop cone for $3.10, a 2-scoop cone for $4.25, a 3-scoop cone for $4.95, and a 4-scoop cone for $5.50. Does the number of scoops and the cost of the cone represent a linear relationship? Justify your answer. If it is linear, can you predict the price of a 6 scoop cone? Page 22
Linear Functions DAY 5 Homework Topic Recognizing Linear Relationships in Contet 4. In middle school math you learned that there is an equation that relates distance, time, and the rate: d = r t. Does this equation represent a linear relationship between time traveled and distance traveled for a given speed? Justify your answer. 5. Come up with your own linear relationship. Justify how you know it is linear. Write a prediction you would have someone make with the information you provide, and then give an answer to your question. 6. Come up with your own non-linear relationship. Justify how you know it is linear. Write a prediction you would have someone make with the information you provide, and then give an answer to your question. Review Questions: 1. Describe the characteristics of the graph of a linear function. (Use the words increasing, decreasing, and rate of change in your answer.) 2. Give an eample of a linear equation and a non-linear equation. How would you eplain to a friend the differences? Page 23